MATH 351 Homework 05

Pick two distributions, across two families of distirbutions. For each of the distributions you choose, do the following.
1. Simulate $501$ convergence paths of means, with two different numbers of random variables $N$ that make up each mean: say $N_2 >> N_1$.
2. Make a histogram of the means for each sample size. Set the keyword argument density of this hist function to True. I also prefer to set histtype to 'step'. Try it, see which histogram you prefer. Overlay the appropriate Normal distribution on your histogram. Make a legend with your various curves appropriately labeled.
3. Plot the empirical distribution function of the means for each sample size. Overlay the cumulative distribution function of the appropriate Normal distribution. Make a legend with your various curves appropriately labeled.
4. What differences do you notice for the different sample sizes?

Here's some code to help.

import scipy.stats as sp
N = sp.norm(3, 10)
N.cdf(2)